Thermodynamic Perturbation\nTheory for Charged Branched\nPolymers

Classical density functional theory (DFT) provides a\nversatile\nframework to study the polymers with complex topological structure.\nGenerally, a classical DFT describes the excess Helmholtz free energy\nof nonbonded chain connectivity due to excluded-volume effects and\nelectrostatic correlations using the first-order thermodynamic perturbation\ntheory (referred to as DFT-TPT1). Beyond first-order perturbation,\nthe second-order TPT (TPT2) captures not only the correlations between\nneighboring monomers but also the interactions within three consecutive\nmonomers, playing a crucial role in describing the polymer topology.\nHowever, the numerical implementation of TPT2 is limited by the lack\nof an effective triple correlation function (CF), especially for charged\nsystems. Here, we propose an effective triple CF and incorporate it\ninto DFT using TPT2 (referred to as DFT-eTPT2) to describe the nonbonded\nchain connectivity due to excluded-volume effects and electrostatic\ncorrelations. Using the data from molecular dynamics simulation as\na benchmark, DFT-eTPT2 shows a clear improvement over DFT-TPT1 in\npredicting the density profiles of both neutral and charged branched\npolymer brushes, accurately capturing key structural features, such\nas the significant peaks near the branching point in the density profiles.\nIn short, this work provides a precise and efficient theoretical tool\nfor revealing molecular-level insights into branched polymers and\ntheir brushes.